Question

Which is a perfect square trinomial
A. X^2 - 169
B. 16x^2 - 3x + 7
C. 4x^2 - 12x + 9
D. 24x + 1

Answer 1

A perfect square trinomial is a polynomial that can be expressed in the form \((ax + b)^2\), which expands to \(a^2x^2 + 2abx + b^2\).

Let's analyze the given options:

A. \(x^2 - 169\)
This is a difference of squares and can be factored as \((x - 13)(x + 13)\). Not a perfect square trinomial.

B. \(16x^2 - 3x + 7\)
This doesn't match the form of a perfect square trinomial upon inspection.

C. \(4x^2 - 12x + 9\)
We can check if this is a perfect square trinomial:
- The first term is \( (2x)^2 \),
- The last term is \(3^2\),
- The middle term should be \(2 \cdot 2x \cdot 3 = 12x\).

Thus, this can be expressed as \((2x - 3)^2\). This is a perfect square trinomial.

D. \(24x + 1\)
This is a linear expression, not a trinomial.

The correct answer is **C. \(4x^2 - 12x + 9\)**.